System and method for calibrating a camera with one-dimensional objects

ABSTRACT

Calibration for a camera is achieved by receiving images of a calibration object whose geometry is one-dimension in space. The received images show the calibration object in several distinct positions. Calibration for the camera is then calculated based on the received images of the calibration object.

RELATED APPLICATIONS

The present application claims priority under 35 U.S.C. §120 as acontinuation of U.S. patent application Ser. No. 10/162,859, filed Jun.3, 2002 now U.S. Pat. No. 7,068,304, the entire disclosure of which ishereby incorporated by reference in its entirety.

TECHNICAL FIELD

This invention relates to computer vision and photogrammetry, and moreparticularly, camera calibration.

BACKGROUND

Camera calibration is a necessary step in three-dimensional (3D)computer vision in order to extract metric information fromtwo-dimensional (2D) images. Much work has been done, starting in thephotogrammetry community [1, 3], and more recently in computer vision[8, 7, 19, 6, 21, 20, 14, 5]. According to the dimension of thecalibration objects, the aforementioned works can be classified intoroughly three categories: (i) 3D reference object based calibration;(ii) 2D plane based calibration; and (iii) self-calibration.

Three-dimensional reference object based camera calibration is performedby observing a calibration object whose geometry in 3-D space is knownwith precision. The calibration object usually consists of two or threeplanes orthogonal to each other. Sometimes, a plane undergoing aprecisely know translation is also used [19], which equivalentlyprovides 3D reference points. These approaches require an expensivecalibration apparatus, and an elaborate setup.

Two-dimensional plane based camera calibration, requires observations ofa planar pattern shown in different orientations [22, 17]. Thistechnique, however, does not lend itself to stereoscopic (or multiple)camera set-ups. For instance, if one camera is mounted in the front of aroom and another in the back of a room, it extremely difficult, if notimpossible, to simultaneously observe a number of different calibrationobjects, to calibrate the relative geometry between the multiplecameras. Of course, this could be performed if the calibration objectswere made transparent, but then the equipment costs would beincrementally higher.

Self-calibration techniques do not use any calibration object. By movinga camera in a static scene, the rigidity of the scene provides ingeneral two constraints [14, 13] on the cameras' internal parametersfrom one camera displacement by using image information alone. If imagesare taken by the same camera with fixed internal parameters,correspondences between three images are sufficient to recover both theinternal and external parameters which allow us to reconstruct 3-Dstructure up to a similarity [10,12]. Although no calibration objectsare necessary, a large number of parameters are estimated, resulting invery expensive computer-implemented computations and a larger percentageof calibration errors.

It is noted that in the preceding paragraphs, as well as the remainderof this specification, the description refers to various individualpublications identified by numeric designator contained within a pair ofbrackets. For example, such a reference may be identified by reciting“reference [1]” or simply “[1]”. Multiple references will be identifiedby a pair of brackets containing more than one designator, for example,[2, 4]. A listing of the publications corresponding to each designatorcan be found at the end of the Detailed Description section.

SUMMARY

A system and method for calibrating a camera is described. In oneimplementation, calibration for a camera is achieved by receiving imagesof a calibration object whose geometry is one-dimension in space. Thereceived images show the calibration object in several distinctpositions. Calibration for a camera is then calculated based on thereceived images of the calibration object.

The following implementations, therefore, introduce the broad concept ofsolving camera calibration by using a calibration object whose geometryis one-dimension in space.

BRIEF DESCRIPTION OF THE DRAWINGS

The detailed description is described with reference to the accompanyingfigures. In the figures, the left-most digit(s) of a reference numberidentifies the figure in which the reference number first appears.

FIG. 1 illustrates an exemplary diagram of a camera calibration system.

FIG. 2 is a flow chart illustrating a process for calibrating a camera.

FIG. 3 is a flow chart illustrating an operation step in FIG. 2 in moredetail.

FIG. 4 shows another view of a calibration object as points C and B movearound point A, which remains fixed.

FIG. 5 is a graph illustrating relative errors for calibration resultsusing a closed-form solution.

FIG. 6 is a graph illustrating the relative errors for calibrationresults using a nonlinear minimization result.

FIG. 7 is table showing data with respect to a camera calibrationexperiment involving a camera calibration system implemented inaccordance with the exemplary descriptions herein.

FIG. 8 illustrates an example of a computing environment within whichthe computer, network, and system architectures described herein can beeither fully or partially implemented.

DETAILED DESCRIPTION

The following discussion is directed to camera calibration usingone-dimensional objects. The subject matter is described withspecificity to meet statutory requirements. However, the descriptionitself is not intended to limit the scope of this patent. Rather, theinventors have contemplated that the claimed subject matter might alsobe embodied in other ways, to include different elements or combinationsof elements similar to the ones described in this document, inconjunction with other present or future technologies.

Calibration System

FIG. 1 illustrates an exemplary diagram of a camera calibration system100. Calibration system 100 includes a computer system 102, a camera 104and a calibration object 106. The computer system 102 is described inmore detail with reference to FIG. 9 and performs camera calibrationcalculations. Based on the camera calibration calculations, the computersystem 102 can send signals (not shown) to the camera 104; the signalsrepresenting values that can be used to calibrate the camera 104. Thecomputer system 102 could also be distributed within a computing systemhaving more than one computing device. See the description of “ExemplaryComputing System and Environment” below for specific examples andimplementations of networks, computing systems, computing devices, andcomponents that can be used to implement the calibration processesdescribed herein.

The camera 104 may be any type of object imaging device such as adigital camera and/or analog camera. As shall become more apparent, morethan one camera can be used in camera calibration system 100. Forinstance, suppose that camera 104 is mounted at the front of a room andanother camera (not shown) is mounted at the back of the room. Bothcameras can then be calibrated by simultaneously imaging the samecalibration object 106. This is very difficult, if not impossible, toachieve with 3D or 2D calibration systems when two or more cameras aremounted at opposite ends of a room. This scenario, however, does notpresent a problem for calibration system 100, because of the ability tocalibrate the camera(s) 104 using calibration object 106 that isone-dimensional and is visible from virtually any point in the space.Camera 104 sends images of the calibration object to computer system 102though any type of connector, such as, for example through a 1394 link.

The calibration object 106 is a one-dimensional (1D) object. In theexemplary illustration, calibration object 106 consists of threecollinear points A, B, and C. The collinear points A, B, and C should bemeasured to provide known relative positions between the points.Moreover, one of the points, as shall be explained in more detail,should remain fixed (i.e., stationary). The points A, B, and C can beimplemented with any inexpensive objects such as a string of beads orballs hanging from a ceiling, or a stick with Styrofoam spheres, etc.The calibration object 106 could also consist of four or more points(not shown), however, camera calibration is not recommended if less thanthree points are used due to having too many unknown parameters, makingthe calibration impossible. The fixed point does not need to be visibleto the camera because it can be computed by intersecting image lines.

FIG. 2 is a flow chart illustrating a process 200 for calibrating acamera 104 in system 100. Process 200 includes various operationsillustrated as blocks. The order in which the process is described isnot intended to be construed as a limitation. Furthermore, the processcan be implemented in any suitable hardware, software, firmware, orcombination thereof. In the exemplary implementation, the majority ofoperations are performed in software (such as in the form of modules orprograms) running on computer system 102.

At block 202, images of the calibration object 106 are received by thecomputer system 102 from camera 104. Based on the received images, thecomputer system 102 is able to provide a calibration solution that canbe used to calibrate camera 104 accordingly (block 204).

Notation & Setups With 1D Calibration Movement

FIG. 3 is a flow chart illustrating the received images operation inmore detail. At blocks 302 and 304, calibration object 106 is movedaround into different configurations while camera 104 images thecalibration object 106. During the movement of the calibration object106, at least one of the points remains fixed. For example, FIG. 4 showsanother view of calibration object 106 as points C and B move aroundpoint A, which remains fixed. Images of the calibration object 106 arethen sent to computer system 102.

To understand block 202 in more detail, reference is made to thenotation used herein. A 2D point is denoted by m=[u, ν]_(T). A 3D pointis denoted by M=[X, Y, Z]^(T). The term {tilde over (x)} is used todenote the augmented vector by adding 1 as the last element: {tilde over(m)}=[u, ν, 1]^(T) and {tilde over (M)}=[X, Z, 1]^(T). A camera ismodeled by the usual pinhole: the relationship between a 3D point M andits image projection m is given bys{tilde over (m)}=A[R t]{tilde over (M)},  1)

-   -   where s is an arbitrary scale factor and (R, t), which is called        the extrinsic parameters, is the rotation and translation which        relates the world coordinate system to the camera coordinate        system. Without loss of generality, in one implementation, the        camera coordinate system is used to define the calibration        object 106, therefore, R=I and t=0 in equation 1 above.        Additionally, matrix A, called the camera intrinsic matrix, is        given by

$\begin{matrix}{A = \begin{bmatrix}\alpha & \gamma & u_{0} \\0 & \beta & v_{0} \\0 & 0 & 1\end{bmatrix}} & (2)\end{matrix}$

-   -   with (u₀, ν₀) the coordinates of the principle point, αand βthe        scale factors in image u and ν axes, and γ the parameter        describing the skewness of the two image axes. The task of        camera calibration is to determine these five intrinsic        parameters.

Finally, the abbreviation A^(−T) will be used for (A⁻¹)^(T) or(A^(T))⁻¹.

As mentioned above calibration is not recommended with free moving 1Dobjects. However, if one of the points remains fixed as shown in FIG. 4,for instance point A is the fixed point, and a is the correspondingimage point, then camera calibration can be realized. We need threeparameters, which are unknown, to specify the coordinates of A in thecamera coordinate system, while image point a provides two scalarequations according to equation 1.

Solving Camera Calibration

By having at least three collinear points (see FIGS. 1 and 4) comprisingthe calibration object 106, the number of unknowns for the pointpositions is 8+2N, where N is the number of observations of thecalibration object 106. This is because given N observations of thecalibration object, we have 5 camera intrinsic parameters, 3 parametersfor the fixed point A, and 2N parameters for the N positions of the freepoint B. For the latter, more explanation is provided here: for eachobservation, we only need 2 parameters to define B because of knowndistance between A and B; no additional parameters are necessary todefine C once A and B are defined. For each observation, b provides twoequations, but c only provides one additional equation, because ofcollinearity of a, b, c. Thus, the total number of equations is 2+3N forN observations. By counting the numbers, if there are six or moreobservations, then it should be possible to solve camera calibration, tobe described in more detail with reference to step 204.

If more than three collinear points are used with know distances, thenumber of unknowns and the number of impendent equations remains thesame, because of cross-ratios. Nevertheless, the more collinear pointsused, the more accurate camera calibration will be, because dataredundancy tends to combat noise in the image data.

After a number of observations of the calibration object have beenreceived by computer system 102 (i.e., block 202 in FIG. 2 and blocks302, 304 in FIG. 3), it is possible to solve for camera calibrationusing a 1D calibration object (block 204 in FIG. 2). Block 204 describesa process for calculating camera calibration, which will be described inmore detail. There are two implementations for solving the calibrationproblem: one involves a closed-form solution and the other involves anon-linear optimization (that is optional, but recommended for greateraccuracy). In this section, both implementations will be described inmore detail with reference to the minimal configuration implementationof the calibration object (three collinear points moving around a fixedpoint, e.g. A).

Referring to FIG. 4, point A is the fixed point in space, and thecalibration object AB moves around A. The length of the calibrationobject measured from A to B is known to be L, i.e.,∥B−A∥=L  (3)The position of point C is know with respect to A and B, and therefore,C=λ _(A) A+λ _(B) B  (4)where λ_(A) and λ_(B) are known. If C is the midpoint of AB, then λ_(A)and λ_(B)=0.5. Points a,b, and c on the image plane 502 are a projectionof space points A, B and C, respectively.

Again, without loss of generality, using the camera calibration systemto define 1D objects, with R=I and t=0 in equation 1. Let the unknowndepths for A, B and C be z_(A), z_(B) and z_(c), respectively. Accordingto equation 1, there areA=z _(A) A ⁻¹ ã  (5)B=z _(B) A ⁻¹ {tilde over (b)}  (6)C=z _(C) A ⁻¹ {tilde over (c)}  (7)Substituting them into (4) yields:z _(C) {tilde over (c)}=z _(A)λ_(A) ãz _(B)λ_(B) {tilde over (b)}  (8)after eliminating A⁻¹ from both sides. By performing a cross-product onboth sides of the equation 8 with {tilde over (c)}, the followingequation is realized:z _(A)λ_(A)(ã×{tilde over (c)})+z _(B)λ_(B)({tilde over (b)}×{tilde over(c)})=0Yielding:

$\begin{matrix}{z_{B} = {{- z_{A}}\frac{{\lambda_{A}\left( {\overset{\sim}{a} \times \overset{\sim}{c}} \right)} \cdot \left( {\overset{\sim}{b} \times \overset{\sim}{c}} \right)}{{\lambda_{B}\left( {\overset{\sim}{b} \times \overset{\sim}{c}} \right)} \cdot \left( {\overset{\sim}{b} \times \overset{\sim}{c}} \right)}}} & (9)\end{matrix}$From equation (3) we have∥A ⁻¹(z _(B) {tilde over (b)}−z _(A) ã)∥=LSubstituting z_(B) by (9) gives:

$z_{A}{{{A^{- 1}\left( {\overset{\sim}{a} + {\frac{{\lambda_{A}\left( {\overset{\sim}{a} \times \overset{\sim}{c}} \right)} \cdot \left( {\overset{\sim}{b} \times \overset{\sim}{c}} \right)}{{\lambda_{B}\left( {\overset{\sim}{b} \times \overset{\sim}{c}} \right)} \cdot \left( {\overset{\sim}{b} \times \overset{\sim}{c}} \right)}\overset{\sim}{b}}} \right.} = L}}$This is equivalent to

$\begin{matrix}{{{z_{A}^{2}h^{- T}A^{- 1}h} = L^{2}}{with}} & (10) \\{h = {\overset{\sim}{a} + {\frac{{\lambda_{A}\left( {\overset{\sim}{a} \times \overset{\sim}{c}} \right)} \cdot \left( {\overset{\sim}{b} \times \overset{\sim}{c}} \right)}{{\lambda_{B}\left( {\overset{\sim}{b} \times \overset{\sim}{c}} \right)} \cdot \left( {\overset{\sim}{b} \times \overset{\sim}{c}} \right)}\overset{\sim}{b}}}} & (11)\end{matrix}$Equation 10 contains the unknown intrinsic parameters A and the unknowndepth, z_(A) of the fixed point A. It is the basic constraint for cameracalibration with 1D objects. Vector h, give by equation 11, can becomputed from image point and known λ_(A) and λ_(B). Since the totalnumber of unknowns is six, it is recommended that at least six imagingobservations of the calibration object 106 be made (that is, sixdifferent configurations of the calibration object). Note that A^(−T)Aactually describes the image of the absolute conic [12].Closed-Form Solution

Let Equation (12) be:

$B = {{{A^{- T}A^{- 1}} \equiv \begin{bmatrix}B_{11} & B_{12} & B_{13} \\B_{12} & B_{22} & B_{23} \\B_{13} & B_{23} & B_{33}\end{bmatrix}} = {\quad{\begin{bmatrix}\frac{1}{\alpha^{2}} & {- \frac{\gamma}{\alpha^{2}\beta}} & \frac{{v_{0}\gamma} - {u_{0}\beta}}{\alpha^{2}\beta} \\{- \frac{\gamma}{\alpha^{2}\beta}} & {\frac{\gamma^{2}}{\alpha^{2}\beta^{2}} + \frac{1}{\beta^{2}}} & {{- \frac{\gamma\left( {{v_{0}\gamma} - {u_{0}\beta}} \right)}{\alpha^{2}\beta^{2}}} - \frac{v_{0}}{\beta^{2}}} \\\frac{{v_{0}\gamma} - {u_{0}\beta}}{\alpha^{2}\beta} & {{- \frac{\gamma\left( {{v_{0}\gamma} - {u_{0}\beta}} \right)}{\alpha^{2}\beta^{2}}} - \frac{v_{0}}{\beta^{2}}} & {\frac{\left( {{v_{0}\gamma} - {u_{0}\beta}} \right)^{2}}{\alpha^{2}\beta^{2}} + \frac{v_{0}^{2}}{\beta^{2}} + 1}\end{bmatrix}.}}}$

Note that B is symmetric, defined by a 6D vectorb=[B ₁₁ ,B ₁₂ , B ₂₂ , B ₁₃ , B ₂₃ , B ₃₃ ] ^(T).  (13)

Let h=[h₁,h₂,h₃]^(T), and x=z_(a) ²b, then equation (10) becomesv ^(T) x=L ²  (14)withν=[h ₁ ²,2h ₁ h ₂ ,h ₂ ²,2h ₁ h ₃,2h ₁ h ₃ ,h ₃ ²]^(T).

When N images of the 1D object are observed, by stacking n suchequations as (14) we haveVx=L ²1  (15)Where V=[v₁, v_(N)]^(T) and 1=[1, 1]^(T). The least-squares solution isthen given byx=L ²(V ^(T) V)⁻¹ V ^(T)1  (16)

Once x is estimated, computer system 102 can compute all the unknownsbased on x=z_(a) ²b. Let x=[x₁, x₂, x₆]^(T). Without difficulty, it ispossible to uniquely extract the intrinsic parameters for the camera andthe depth z_(A) as:

$\begin{matrix}{v_{0} = {\left( {{x_{2}x_{4}} - {x_{1}x_{5}}} \right)/\left( {{x_{1}x_{3}} - x_{2}^{2}} \right)}} \\{z_{A} = \sqrt{x_{6} - {\left\lbrack {x_{4}^{2} + {v_{0}\left( {{x_{2}x_{4}} - {x_{1}x_{5}}} \right)}} \right\rbrack/x_{1}}}} \\{\alpha = \sqrt{z_{A}/x_{1}}} \\{\beta = \sqrt{z_{A}{x_{1}/\left( {{x_{1}x_{3}} - x_{2}^{2}} \right)}}} \\{\gamma = {x_{2}\alpha^{2}{\beta/s_{A}}}} \\{u_{0} = {{\gamma\;{v_{0}/\alpha}} - {x_{4}{\alpha^{2}/z_{A}}}}}\end{matrix}$

At this point, it is possible for the computer system 102 to computez_(B) according to equation (9), so points A and B can be computed fromequations (5) and (6), while point C can be computed according toequations (3).

Nonlinear Optimization

In block 204, it is possible to refine the above calibration solutionsthrough a maximum likelihood inference.

Supposing there are N images of the calibration object 106 and there arethree points on the comprising the object. Point A is fixed, and pointsB and C move around A. Assume that the images points are corrupted byindependent and identically distributed noise. The maximum likelihoodestimate can be obtained by minimizing the following functional:

$\begin{matrix}{\sum\limits_{i = 1}^{N}\;\left( {{{a_{i} - {\phi\left( {A,A} \right)}}}^{2} + {{b_{i} - {\phi\left( {A,B_{i}} \right)}}}^{2} + {{c_{i} - {\phi\left( {A,C_{i}} \right)}}}^{2}} \right)} & (17)\end{matrix}$where φ(A,M)(M∈{A,B_(i),C_(i)}) is the projection of point M onto theimage, according to equations (5) to (6). More precisely,

${{\phi\left( {A,M} \right)} = {\frac{1}{z_{M}}{AM}}},$wherez_(M) is the z-component of M.

The unknowns to be estimated are: five camera intrinsic parametersα,β,γ,u₀ and ν₀ that define matrix A; three parameters for thecoordinates of the fixed point A; and two N additional parameters todefined points B_(i) and C_(i) at each instant. Therefore there are atotal of 8+2N unknowns. Regarding the parameterization for B and C, weuse the spherical coordinates φ and θ to define the direction of thecalibration object 106, and point B is then given by:

$B = {A + {L\begin{bmatrix}{\sin\;\theta\;\cos\;\phi} \\{\sin\;\theta\;\sin\;\phi} \\{\cos\;\theta}\end{bmatrix}}}$where L is the known distance between A and B. In turn, point C iscomputed according to equation (4). Therefore, only two additionalparameters are needed for each observation.

Minimizing equation (17) is a nonlinear minimization problem, which issolved with the Levenberg-Marquardt Algorithm as implemented in Minpack[15]. This algorithm requires an initial guess of A, A, {B_(i),C_(i)|i=1 . N}, which can be obtained using the closed-form solutiondescribed earlier.

Experimental Results

Using computer simulations suppose that a simulated camera 104 has thefollowing properties: α=1000,β=1000,γ=0, u₀=320 and ν₀=240. The imageresolution is 640×480. A calibration object 106 in the form of a stickis 70 cm long and is also simulated. The object has a fixed point A at[0, 35, 150]^(T). The other endpoint of the object is B, and C islocated at the half way point between A and B. One hundred randomorientations of the calibration object 106 are generated by sampling θin [π/6,5π,6] and φ in [π,2π] according to uniform distribution. PointsA, B, and C are then projected onto the image 402.

Gaussian noise with 0 mean and σ standard deviation is added to theprojected image points a, b and c. The estimated camera parameters arecompared with the ground truth, and their relative errors are measuredwith respect to focal length α. Note that the relative errors in (u₀,ν₀) with respect to α, are as proposed by Triggs in [18]. Triggs pointedout that the absolute errors in (u₀, ν₀) is not geometricallymeaningful, while computing the relative error is equivalent tomeasuring the angle between the true optical axis and the estimated one.

The noise level is varied from 0.1 pixels to 1 pixel. For each noiselevel, the calibration system 100 performs 120 independent trials, andthe results as shown in FIGS. 5 and 6, are the average. FIG. 5 is agraph illustrating relative errors for calibration results using theclosed-form solution. FIG. 6 is a graph illustrating the relative errorsfor calibration results using the nonlinear minimization result. Errorsincrease almost linearly with the noise level. The nonlinearminimization refines the closed-form solution, and producessignificantly better results (with 50% less errors). At 1 pixel noiselevel, the errors for the closed-form solution are about 12% while thosefor the nonlinear minimization are about 6%.

Using actual real data, three toy beads were stung together with a stickto form the calibration object 106. The beads are approximately 14 cmapart (i.e., L =28). The stick was then moved around while fixing oneend with the aid of a book. A video of 150 frames was recorded. A beadin the image is modeled as Gaussian blob in the RGB space, and thecentroid of each detected blob is the image point we use for cameracalibration. The proposed algorithm is therefore applied to the 150observations of the beads, and the estimated parameters are provided ina table shown in FIG. 7. The first row is the estimation from theclosed-form solution, while the second row is the refined result afternonlinear minimization. For the image skew parameter γ, the anglebetween the image axes are also provided in parenthesis (it should beclose to 90 degrees).

For comparison, a plane-based calibration technique described in [22]was used to calibrate the same camera. Five images of a planar patternwere taken. The calibration result is shown in the third row of the FIG.7. The fourth row displays the relative difference between theplane-based result and the nonlinear solution with respect to the focallength (828.92). There is about a two percent difference between thecalibration techniques, which can be attributed to noise, imprecision ofthe extracted data points and a rudimentary experimental setup.Nevertheless, despite these non-ideal factors, the calibration resultsusing a one-dimensional object are very encouraging.

Exemplary Computing System and Environment

FIG. 8 illustrates an example of a computing environment 800 withinwhich the computer, network, and system architectures (such as cameracalibration system 100) described herein can be either fully orpartially implemented. Exemplary computing environment 800 is only oneexample of a computing system and is not intended to suggest anylimitation as to the scope of use or functionality of the networkarchitectures. Neither should the computing environment 800 beinterpreted as having any dependency or requirement relating to any oneor combination of components illustrated in the exemplary computingenvironment 800.

The computer and network architectures can be implemented with numerousother general purpose or special purpose computing system environmentsor configurations. Examples of well known computing systems,environments, and/or configurations that may be suitable for useinclude, but are not limited to, personal computers, server computers,thin clients, thick clients, hand-held or laptop devices, multiprocessorsystems, microprocessor-based systems, set top boxes, programmableconsumer electronics, network PCs, minicomputers, mainframe computers,gaming consoles, distributed computing environments that include any ofthe above systems or devices and the like.

The camera calibration methodologies may be described in the generalcontext of computer-executable instructions, such as program modules,being executed by a computer. Generally, program modules includeroutines, programs, objects, components, data structures, etc. thatperform particular tasks or implement particular abstract data types.The camera calibration methodologies may also be practiced indistributed computing environments where tasks are performed by remoteprocessing devices that are linked through a communications network. Ina distributed computing environment, program modules may be located inboth local and remote computer storage media including memory storagedevices.

The computing environment 800 includes a general-purpose computingsystem in the form of a computer 802. The components of computer 802 caninclude, by are not limited to, one or more processors or processingunits 804, a system memory 806, and a system bus 808 that couplesvarious system components including the processor 804 to the systemmemory 806.

The system bus 808 represents one or more of any of several types of busstructures, including a memory bus or memory controller, a peripheralbus, an accelerated graphics port, and a processor or local bus usingany of a variety of bus architectures. By way of example, sucharchitectures can include an Industry Standard Architecture (ISA) bus, aMicro Channel Architecture (MCA) bus, an Enhanced ISA (EISA) bus, aVideo Electronics Standards Association (VESA) local bus, and aPeripheral Component Interconnects (PCI) bus also known as a Mezzaninebus.

Computer system 802 typically includes a variety of computer readablemedia. Such media can be any available media that is accessible bycomputer 802 and includes both volatile and non-volatile media,removable and non-removable media. The system memory 806 includescomputer readable media in the form of volatile memory, such as randomaccess memory (RAM) 810, and/or non-volatile memory, such as read onlymemory (ROM) 812. A basic input/output system (BIOS) 814, containing thebasic routines that help to transfer information between elements withincomputer 802, such as during start-up, is stored in ROM 812. RAM 810typically contains data and/or program modules that are immediatelyaccessible to and/or presently operated on by the processing unit 804.

Computer 802 can also include other removable/non-removable,volatile/non-volatile computer storage media. By way of example, FIG. 8illustrates a hard disk drive 816 for reading from and writing to anon-removable, non-volatile magnetic media (not shown), a magnetic diskdrive 818 for reading from and writing to a removable, non-volatilemagnetic disk 820 (e.g., a “floppy disk”), and an optical disk drive 822for reading from and/or writing to a removable, non-volatile opticaldisk 824 such as a CD-ROM, DVD-ROM, or other optical media. The harddisk drive 816, magnetic disk drive 818, and optical disk drive 822 areeach connected to the system bus 808 by one or more data mediainterfaces 826. Alternatively, the hard disk drive 816, magnetic diskdrive 818, and optical disk drive 822 can be connected to the system bus808 by a SCSI interface (not shown).

The disk drives and their associated computer-readable media providenon-volatile storage of computer readable instructions, data structures,program is modules, and other data for computer 802. Although theexample illustrates a hard disk 816, a removable magnetic disk 820, anda removable optical disk 824, it is to be appreciated that other typesof computer readable media which can store data that is accessible by acomputer, such as magnetic cassettes or other magnetic storage devices,flash memory cards, CD-ROM, digital versatile disks (DVD) or otheroptical storage, random access memories (RAM), read only memories (ROM),electrically erasable programmable read-only memory (EEPROM), and thelike, can also be utilized to implement the exemplary computing systemand environment.

Any number of program modules can be stored on the hard disk 816,magnetic disk 820, optical disk 824, ROM 812, and/or RAM 810, includingby way of example, an operating system 826, one or more applicationprograms 828, other program modules 830, and program data 832. Each ofsuch operating system 826, one or more application programs 828, otherprogram modules 830, and program data 832 (or some combination thereof)may include an embodiment of the camera calibration methodologies.

Computer system 802 can include a variety of computer readable mediaidentified as communication media. Communication media typicallyembodies computer readable instructions, data structures, programmodules, or other data in a modulated data signal such as a carrier waveor other transport mechanism and includes any information deliverymedia. The term “modulated data signal” means a signal that has one ormore of its characteristics set or changed in such a manner as to encodeinformation in the signal. By way of example, and not limitation,communication media includes wired media such as a wired network ordirect-wired connection, and wireless media such as acoustic, RF,infrared, and other wireless media. Combinations of any of the above arealso included within the scope of computer readable media.

A user can enter commands and information into computer system 802 viainput devices such as a keyboard 834 and a pointing device 836 (e.g., a“mouse”). Other input devices 838 (not shown specifically) may include amicrophone, joystick, game pad, satellite dish, serial port, scanner,and/or the like. These and other input devices are connected to theprocessing unit 804 via input/output interfaces 840 that are coupled tothe system bus 808, but may be connected by other interface and busstructures, such as a parallel port, game port, or a universal serialbus (USB).

A monitor 842 or other type of display device can also be connected tothe system bus 808 via an interface, such as a video adapter 844. Inaddition to the monitor 842, other output peripheral devices can includecomponents such as speakers (not shown) and a printer 846 which can beconnected to computer 802 via the input/output interfaces 840.

Computer 802 can operate in a networked environment using logicalconnections to one or more remote computers, such as a remote computingdevice 848. By way of example, the remote computing device 848 can be apersonal computer, portable computer, a server, a router, a networkcomputer, a peer device or other common network node, and the like. Theremote computing device 848 is illustrated as a portable computer thatcan include many or all of the elements and features described hereinrelative to computer system 802.

Logical connections between computer 802 and the remote computer 848 aredepicted as a local area network (LAN) 850 and a general wide areanetwork (WAN) 852. Such networking environments are commonplace inoffices, enterprise-wide computer networks, intranets, and the Internet.When implemented in a LAN networking environment, the computer 802 isconnected to a local network 950 via a network interface or adapter 854.When implemented in a WAN networking environment, the computer 802typically includes a modem 856 or other means for establishingcommunications over the wide network 852. The modem 856, which can beinternal or external to computer 802, can be connected to the system bus808 via the input/output interfaces 840 or other appropriate mechanisms.It is to be appreciated that the illustrated network connections areexemplary and that other means of establishing communication link(s)between the computers 802 and 848 can be employed.

In a networked environment, such as that illustrated with computingenvironment 800, program modules depicted relative to the computer 802,or portions thereof, may be stored in a remote memory storage device. Byway of example, remote application programs 858 reside on a memorydevice of remote computer 848. For purposes of illustration, applicationprograms and other executable program components, such as the operatingsystem, are illustrated herein as discrete blocks, although it isrecognized that such programs and components reside at various times indifferent storage components of the computer system 802, and areexecuted by the data processor(s) of the computer.

References

[1] Duane C. Brown. Close-range camera calibration. PhotogrammetricEngineering, 37(8):855-866,1971.

[2] Bruno Caprile and Vincent Torre. Using Vanishing Points for CameraCalibration. The International Journal of Computer Vision, 4(2):127-140,March 1990.

[3] W. Faig. Calibration of close-range photogrammetry systems:Mathematical formulation. Photogrammetric Engineering and RemoteSensing, 41(12):1479-1486, 1975.

[4] Oliver Faugeras. Three-Dimensional Computer Vision: a GeometricViewpoint. MIT Press, 1993.

[5] Oliver Faugeras, Tuan Luong, and Steven Maybank. Cameraself-calibration: theory and experiments. In G. Sandini, editor, Proc2nd ECCV, volume 588 of Lecture Notes in Computer Science, pages321-334, Santa Margherita Ligure, Italy, May 1992. Springer-Verlag.[6] Oliver Faugeras and Giorgio Toscani. The calibration problem forstereo. In Proceedings of the IEEE Conference on Computer Vision andPattern Recognition, pages 15-20, Miami Beach, Fla., June 1986. IEEE.[7] S. Ganapathy. Decomposition of transformation matrices for robotvision. Pattern Recognition Letters, 2:401-412, December 1984.[8] D. Gennery. Stereo-camera calibration. In Proceedings of the 10thImage Understanding Workshop, pages 101-108, 1979.[9] Richard Hartley. Self-calibration from multiple views with arotating camera. In J- O. Eklundh, editor, Proceedings of the 3rdEuropean Conference on Computer Vision, volume 800-801 of Lecture Notesin Computer Science, pages 471-478, Stockholm, Sweden, May 1994.Springer-Verlag.[10] Richard I. Hartley. An algorithm for self calibration from severalviews. In Proceedings of the IEEE Conference on Computer Vision andPattern Recognition, pages 808-912, Seattle, Wash., June 1994. IEEE.[11] D. Liebowitz and A. Zisserman. Metric rectification for perspectiveimages of planes. In Proceedings of the IEEE Conference on ComputerVision and Pattern Recognition, pages 482-488, Santa Barbara, Calif.,June 1998. IEEE Computer Society.[12] Q. -T. Luong and O. D. Faugeras. Self-calibration of a movingcamera from point correspondences and fundamental matrices. TheInternational Journal of Computer Vision, 22(3):261-289, 1997.[13] Quang-Tuan Luong. Matrice Fondamentale et Calibration Visuelle surl'Environment-Vers une plus grande autonomie des systèmes robotiques,PhD thesis, Université de Paris-Sud, Center d'Orsay, December 1992.[14] S. J. Maybank and O. D. Faugeras. A theory of self-calibration of amoving Camera. The International Journal of Computer Vision,8(2):123-152, August 1992.[15] J. J. More. The levenberg-marquardt algorithm, implementation andtheory. In G. A. Watson, editor, Numerical Analysis, Lecture Notes inMathematics 630. Springer-Verlag, 1977.[16] G. Stein. Accurate internal camera calibration using rotation, withanalysis of sources of error. In Proc. Fifth International Conference onComputer Vision, pages 230-236, Cambridge, Mass., June 1995.[17] P. Sturm and S. Maybank. On plane-based camera calibration: Ageneral algorithm, singularities, applications. In Proceedings of theIEEE Conference on Computer Vision and Pattern Recognition, pages432-437, Fort Collins, Colo., June 1999. IEEE Computer Society Press.[18] B. Triggs. Autocalibration from planar scenes. In Proceedings ofthe 5th European Conference on Computer Vision, pages 89-105, Freiburg,Germany, June 1998.[19] Roger Y. Tsai. A versatile camera calibration technique forhigh-accuracy 3D machine vision metrology using off-the-shelf tv camerasand lenses. IEEE Journal of Robotics and Automation, 3(4):323-344,August 1987.[20] G. Q. Wei and S. D. Ma. A complete two-plane camera calibrationmethod and experimental comparisons. In Proc. Fourth InternationalConference on Computer Vision, pages 439-446, Berlin, May 1993.[21] J. Weng, P. Cohen, and M. Herniou. Camera calibration withdistortion models and accuracy evaluation. IEEE Transactions on PatternAnalysis and Machine Intelligence, 14(10):965-980, October 1992.[22] Z. Zhang. A flexible new technique for camera calibration. IEEETransactions on Pattern Analysis and Machine Intelligence,22(11):1330-1334, 2000.

CONCLUSION

Although the invention has been described in language specific tostructural features and/or methodological acts, it is to be understoodthat the invention defined in the appended claims is not necessarilylimited to the specific features or acts described. Rather, the specificfeatures and acts are disclosed as exemplary forms of implementing theclaimed invention.

1. In a computer system, a method comprising: receiving images of acalibration object whose geometry is one-dimension in space, thereceived images showing the calibration object in six or more distinctconfigurations, wherein: the calibration object comprises three or morecollinear points with known relative positions between the points; andat least one of the collinear points remains fixed with respect to theother points in the received images showing the calibration object inseveral distinct position; and calculating a calibration for a camerabased on the received images of the calibration object.
 2. One or morecomputer-readable media comprising computer-executable instructionsthat, when executed, perform the method as recited in claim
 1. 3. Amethod, comprising: imaging a one-dimensional object in six or moredistinct configurations, the imaging performed by an object imagingdevice, wherein the one-dimensional object comprises three or morecollinear points with known relative positions between the points andwherein at least one of the collinear points remains fixed with respectto the other points in the received images showing the calibrationobject in several distinct positions; and estimating unknown parametersassociated with object imaging device by computing parameters associatedwith imaging the one-dimensional object in the six or more distinctconfigurations.
 4. The method as recited in claim 3, further comprisingcalculating unknown parameters associated with the object imaging deviceand the one-dimensional object using a closed-form equation.
 5. Themethod as recited in claim 3, further comprising calculating unknownparameters associated with the object imaging device and theone-dimensional object using a non-linear solution.
 6. One or morecomputer-readable media comprising computer-executable instructionsthat, when executed, perform the method as recited in claim
 3. 7. Asystem, comprising: means for imaging a one-dimensional object in six ormore distinct configurations; and means for estimating unknownparameters associated with object imaging device by computing parametersassociated with imaging the one-dimensional object in the six or moredistinct configurations, wherein the one-dimensional object comprisesthree or more collinear points with known relative positions between thepoints and wherein at least one of the collinear points is fixed.
 8. Thesystem as recited in claim 7, wherein the means for imaging theone-dimensional object is an object imaging device.
 9. The system asrecited in claim 7, further comprising means for calculating unknownparameters associated with the object imaging device and theone-dimensional object using a closed-form equation.
 10. The method asrecited in claim 7, further comprising calculating unknown parametersassociated with the object imaging device and the one-dimensional objectusing a non-linear solution.